State-selective Electron Capture Cross Sections Research Articles

Electron capture and ionisation in He^{2+} collisions with H_2

State-selective non-dissociative electron capture and ionisation cross sections are calculated for collisions between bare helium-ions and molecular hydrogen. The two-centre wave-packet convergent close-coupling approach is used and the hydrogen molecule is represented as an effective one-electron target. For the electron-capture cross section, our results are in good agreement with experimental measurements at energies above 100 keV/u. However, near the peak of the cross section, they are larger than the experimental data. The total ionisation cross section is also in good agreement with experiment, particularly at low and high energies. The results for the state-selective electron-capture cross section are generally in good agreement with the limited experimental measurements. However, we find that our results appear to consistently overestimate the experimental data for electron capture into the s states at intermediate energies. The present results are the first calculations capable of producing electron capture and ionisation cross sections over a wide incident energy range within a single unified theoretical framework.Graphical

State-selective electron capture cross sections in collision between fully striped ions and ground state hydrogen atom—Classical treatment of the collision

We present a state-selective electron capture cross sections database from the ground state hydrogen atom. A standard three-body classical trajectory Monte Carlo (CTMC) and quasi-classical trajectory Monte Carlo (QCTMC) models were employed for impact energies between 10 and 200 keV/amu. The projectile ions are H+, He2+, Li3+, Be4+, B5+, C6+, N7+, and O8+. The cross sections are tabulated for each value of the final quantum numbers n, l, m, summed over m for the given n and l and over l and m for the given n. The maximum quantum number nmax is set to 4 for H+, He2+ and Li3+, as well as to 5 for Be4+, B5+, C6+, N7+ and O8+, respectively.

State selective classical electron capture cross sections in Be4+ \u2009+\u2009H(1s) collisions with mimicking quantum effect

We present state-selective electron capture cross sections in collision between Be4+ and ground state hydrogen atom. The n- and nl-selective electron capture cross sections are calculated by a three-body classical trajectory Monte Carlo method (CTMC) and by a classical simulation schema mimicking quantum features of the collision system. The quantum behavior is taken into account with the correction term in the Hamiltonian as was proposed by Kirschbaum and Wilets (Phys Rev A 21:834, 1980). Calculations are carried out in the projectile energy range of 1–1000 keV/amu. We found that our model for Be4+ + H(1s) system remarkably improves the obtained state-selective electron capture cross sections, especially at lower projectile energies. Our results are very close and are in good agreement with the previously obtained quantum–mechanical results. Moreover, our model with simplicity can time efficiently carry out simulations where maybe the quantum mechanical ones become complicated, therefore, our model should be an alternative way to calculate accurate cross sections and maybe can replace the quantum–mechanical methods.

Electron capture and 2s→2p excitation in Be3+-Li collisions

The electron capture and 2s→2p excitation processes in Be3+-Li collisions are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method and by the two-center atomic orbital close-coupling (TC-AOCC) method in the energy ranges 10−4–1.2 keV/u and 0.5–100 keV/u, respectively. Spin-resolved total, n-shell and state-selective electron capture cross sections are calculated with large expansion of the MO and AO basis sets. In the overlapping energy range the results of the two sets of calculations for the total and n = 4, 3-shell capture cross sections agree very well for both singlet and triplet channels. Good agreement in this energy range between the two calculations is obtained also for the spin-resolved cross sections except some weak reaction channels. It is found that the total and n = 4 shell singlet and triplet capture cross sections differ significantly from each other in the energy region below 0.1 keV/u, and especially for the 4l cross sections this difference becomes considerable at 1 keV/u. For the weak n = 3 and n = 2 capture channels the difference between singlet and triplet cross sections is much smaller. The excitation 2s-2p cross section for Li in this collision system has also been calculated and no significant difference between the singlet and triplet cross sections was found in the entire energy range considered.

Electron capture, excitation and ionization in H+–Be+ collisions

State-selective single electron capture, excitation and ionization processes in proton collisions with Be+(1s22s) and Be+(1s22p) ions are studied by using the quantum-mechanical molecular orbital (QMOCC) and the two-center atomic orbital close-coupling (TC-AOCC) methods in the combined energy range 0.01–300 keV/u. In the QMOCC calculations six 2Σ+ and three 2Π states are included in the expansion basis. The TC-AOCC expansion basis includes 35 discrete states centered on the proton and 182 states on Be2+ out of which 88 are continuum pseudostates. The atomic states on Be2+ are generated by a one-electron model potential for the electron interaction with Be2+ ion core that reproduces the exact energies with accuracy better than 0.5%. Total and state-selective electron capture and excitation cross sections to final states with n ≤ 4 are presented. The sum of the cross sections for the transitions to continuum pseudostates (ionization cross section) is also reported for both initial target states. The physical mechanisms involved in the dynamics of considered processes are discussed in detail at both low and high energies. The reported cross sections should be useful in the kinetic modeling and diagnostics of edge plasmas in present magnetic fusion experiments, as well as in the current ITER design, in which beryllium is used as first wall material.

Electron capture and excitation in H+ − Li+ collisions

The processes of state-selective electron capture and excitation in proton collisions with Li+(1s2 1S) and Li+(1s2s 1,3S) ions are studied by using the two-center atomic orbital close-coupling (TC-AOCC) methods in the energy range 2.5–800 keV. The interaction of the active electron with the Li2+ ion core is represented by model potentials that reproduce the energies of excited singlet and triplet states of Li+ with accuracy better than 2%. The expansion basis in the coupled state calculations includes all states with n ≤ 8 (in total 120 states) centered on each of the colliding centers. Total and state-selective electron capture and excitation cross sections to final states with n ≤ 4 are presented. The physical mechanisms involved in the dynamics of considered processes are discussed in detail. The reported cross sections should be useful in the kinetic modeling and diagnostics of fusion reactor plasmas with liquid lithium divertors.

Electron capture and excitation processes in H+−H collisions in dense quantum plasmas

Electron capture and excitation processes in proton–hydrogen atom collisions taking place in dense quantum plasmas are studied by employing the two-centre atomic orbital close-coupling (TC-AOCC) method. The Debye–Hückel cosine (DHC) potential is used to describe the plasma screening effects on the Coulomb interaction between charged particles. The properties of a hydrogen atom with DHC potential are investigated as a function of the screening strength of the potential. It is found that the decrease in binding energy of nl levels with increasing screening strength is considerably faster than in the case of the Debye–Hückel (DH) screening potential, appropriate for description of charged particle interactions in weakly coupled classical plasmas. This results in a reduction in the number of bound states in the DHC potential with respect to that in the DH potential for the same plasma screening strength, and is reflected in the dynamics of excitation and electron capture processes for the two screened potentials. The TC-AOCC cross sections for total and state-selective electron capture and excitation cross sections with the DHC potential are calculated for a number of representative screening strengths in the 1–300 keV energy range and compared with those for the DH and pure Coulomb potential. The total capture cross sections for a selected number of screening strengths are compared with the available results from classical trajectory Monte Carlo calculations.

Cross sections for electron capture and excitation in proton collisions with the metastable Be(2s2p3P) atom

The two-center atomic orbital close-coupling method is employed to study electron capture and excitation processes in proton collisions with the metastable Be(1s2s2p P) atom. The interaction of the active electron with the Be ion core is represented by a model potential reproducing accurately (to within 3.5%) the energies of triplet excited states Be(1s2snl L) (at least up to n = 7). The excitation and state-selective electron capture cross sections up to the n = 5 shells of both centers are calculated in the energy range 1–200 keV/u using an expansion basis involving all the states with n ≤ 7 on H and all triplet states with n ≤ 7 on Be, augmented with a number of pseudostates. In the energy region below ~10 keV/u, the cross sections of both processes exhibit oscillatory structures, resulting from the multistate coupling accounted for in the dynamical model. It has been found that the magnitude of excitation cross sections above ~10 keV/u is dominated by the multipole interactions, while below this energy the excitation process proceeds through intermediate electron capture states.

State-selective electron capture in collisions of C6+, N7+ with Hydrogen at intermediate energies

We present a joint study of the electron capture process in multicharged ions on atomic Hydrogen at intermediate energies. We have applied two methods, the Eikonal Impulse Approximation (EIA) and the hydrogenic-Classical Trajectory Monte Carlo (CTMC) method. Good agreement is found in both total and state-selective electron capture cross sections.

Single- and double-electron-capture processes in the collisions of C4+ions with He

The nonradiative single-electron-capture (SEC) and double-electron-capture (DEC) processes for C${}^{4+}$(1${s}^{2}$) colliding with He atoms are investigated by using the quantum-mechanical molecular-orbital close-coupling method. Total and state-selective electron-capture cross sections are calculated in the energy range of 10${}^{\ensuremath{-}6}$--6 keV/amu. For energies less than 2 keV/amu, the DEC dominates the electron-capture processes. As the energy increases, the SEC cross sections increase while the DEC cross sections decrease; when $E$ g 2 keV/amu, the SEC process becomes the dominant mechanism. It is found that the SEC processes mainly result from the electron capture to $n$ = 3 channels of C${}^{3+}$ ion for energy below 0.7 keV/amu and from $n$ = 2 channels for $Eg0.7$ keV/amu. Compared with the available theoretical calculations, better agreement is achieved between the present results and the available measurements for total DEC and SEC cross sections. For state-resolved cross sections, excellent agreement is obtained for two-electron capture to C${}^{2+}$(2${s}^{2}$), C${}^{2+}$(2$s$2$p$), and C${}^{2+}$(2${p}^{2}$) and one-electron capture to C${}^{3+}$(2$s$) and C${}^{3+}$(2$p$) between the present calculations and the available theoretical and experimental results.

Angular- and state-selective differential cross sections for single-electron capture inp-He collisions at intermediate energies

State-selective electron capture cross sections and projectile scattering-angle differential cross sections for single-electron capture in collisions of protons with He at energies ranging from 50 to 100 keV have been experimentally investigated by means of a reaction microscope. It is shown that for single-electron capture the ground-state transfer is the dominant reaction channel, and excited-state transfer has relative small contributions to the cross sections. The transfer-excitation process has a minor contribution to the total cross sections. As the projectile energy increases, ground-state transfer remains dominant, but the relative contributions of the excited-state transfers become more important. The minor contribution of transfer excitation remains almost unchanged. Furthermore, it was found that for single transfer the present results are in good agreement with independent electron model predictions in the energy regime considered. For transfer excitation, however, there are obvious discrepancies between our measurements and theoretical results. We concluded that the electron-electron-correlation effects may play a role at least in transfer excitation in collisions of protons with He in the energy range considered.

Electron capture and excitation in slow H+-He(21,3L) collisions

Dynamics of electron capture and excitation processes in collisions of H${}^{+}$ with the excited He(2 ${}^{1,3\phantom{\rule{-0.16em}{0ex}}}{L}_{m}$) atom ($L$ $=$ $S$,$P$) has been studied by using the full quantum-mechanical molecular orbital close-coupling (QMOCC) method with ab initio determined molecular states. 38 singlet and 37 triplet molecular states of the HeH${}^{+}$ system, that asymptotically correlate to the $n$ $=$ 1--4 projectile and target atomic states, have been included in the expansion basis. The shell- and state-selective electron capture and excitation cross sections have been calculated in the 0.01--6 keV/u energy range up to the $n$ $=$ 4 shell and their energy behavior discussed on the basis of identified reaction mechanisms.

State-selective electron capture in N5+-H and O6+-H collisions

The two-centre atomic orbital close-coupling method is employed to study the electron capture reactions in collisions of N5+ and O6+ ions with ground state atomic hydrogen in the energy range from 0.5 to 200 keV u−1. The interaction of an active electron with the projectile ion is represented by a model potential. Total and state-selective electron capture cross sections for the dominant and subdominant reaction channels are calculated and compared with the available experimental and theoretical data.

Dynamics ofO6+ + H electron capture in Debye plasmas and properties of resultingO5+(nl) emission spectra

The electron capture in ${\mathrm{O}}^{6+}$-H collisions is studied by the two-center atomic orbital close-coupling (TC-AOCC) method when the interactions of charged particles are screened and have a Yukawa form. Atomic orbitals and eigenenergies of $n$ $\ensuremath{\leqslant}$ $6$ states on ${\mathrm{O}}^{5+}$ and $n$ $\ensuremath{\leqslant}$ $2$ states on H are calculated as a function of the interaction screening parameter and used in the AOCC dynamics scheme to calculate the electron capture cross sections in the energy range $1$--$200$ keV/u. It is shown that the degree of interaction screening reduces the electron binding energies, the number of open electron capture channels, and the strength of exchange couplings, thus affecting the entire collision dynamics and the magnitude and energy behavior of electron capture cross sections. The state-selective electron capture cross sections in this collision system, as well as the intensities of a number of charge exchange spectral lines, for a number of representative interaction screening strengths are presented and discussed.

Electron capture in C6+ + H collisions in Debye plasmas

The electron capture in C6+–H collisions taking place in a weakly coupled plasma is studied by the two-centre atomic orbital close-coupling method. The interaction between charged particles is represented by the Debye–Hückel potential, appropriate for weakly coupled (Debye) plasmas. The adopted two-centre expansion basis contains all the states with n ⩽ 8 centred on C6+ and all the states with n ⩽ 2 centred on H+. The coupled channel calculations have been performed in the 0.5–100 keV/u energy range in which the results with the adopted basis are convergent. It is shown that the electron capture dynamics in Debye plasmas is strongly affected by the plasma screening of charged particle interactions mainly due to the reduction of electron binding energy and the number of reaction channels when the plasma screening increases. These effects are illustrated on the state-selective electron capture cross sections for a number of representative values of the interaction screening parameter and on the properties of a number of charge exchange spectral lines.

State-selective charge exchange from H(1s), H(n = 2), Li and Na targets by very highly charged ions

In order to provide information for charge exchange spectroscopy diagnostics in new, high temperature tokamak plasmas, n-level state-selective electron capture cross sections are presented for very highly charged ions with charge states q ⩾ 10. Fully stripped ions with charges of 10+, 18+, 26+, 54+ and 92+ are considered in order to provide scaling information over a broad range. The H(1s) and H(n = 2) targets are evaluated at 1, 10 and 100 keV/amu, i.e. plasma core temperatures to those encountered during neutral beam heating. For use in pellet diagnostics, cross sections are given for Li and Na targets at 10 keV/amu. These latter targets also provide a means to experimentally test the accuracy of the H(n = 2) results since they are pseudo-one-electron atoms with ionization energies close to that of excited hydrogen.

Dynamics ofO8++Helectron capture in Debye plasmas

The electron capture in ${\text{O}}^{8+}\ensuremath{-}\text{H}$ collisions is studied by the two-center atomic-orbital close-coupling method when the interactions of charged particles are screened and have a Yukawa form. Atomic orbitals and eigenenergies of $n\ensuremath{\le}7$ states on ${\text{O}}^{7+}$ and $n\ensuremath{\le}2$ states on H are calculated as a function of the interaction screening parameter and used in the atomic-orbital close-coupling dynamics scheme to calculate the electron capture cross sections in the energy range of 0.2--50 keV/u. It is shown that the degree of interaction screening determines the reduction in electron binding energies, the number of open electron capture channels, and the strength of the exchange couplings, thus affecting the entire collision dynamics and the magnitude and energy behavior of state-selective cross sections. The changes in electron binding energies and capture cross sections when the interaction screening varies introduce dramatic changes in the radiation spectrum of ${\text{O}}^{7+}(nl)$ capture states with respect to the unscreened interaction case. The state-selective electron capture cross sections in this collision system, as well as the intensities of a number of charge exchange spectral lines, for a number of representative screening parameter values are presented and discussed.

Atomic collisions with screened Coulomb interactions: excitation and electron capture in H+ + H collisions

Dynamics of excitation and electron capture processes in the H+ + H(1s) collision system in a Debye plasma is studied as an example of collision systems with screened Coulomb interactions. The two-centre atomic orbital close-coupling method (TC-AOCC) was used with a basis containing all n ⩽ 6 and 7s discrete and 99 quasi-continuum states centred on the target and all n ⩽ 3 discrete states centred on the projectile when describing the excitation process, and vice versa when describing the electron capture. The atomic orbitals and energies of all one-centre states have been determined variationally as a function of screening parameter and used to calculate the state-selective electron capture and excitation cross sections. With an increase of the screening, the bound states successively enter the continuum, thereby reducing the number of reaction channels in the discrete spectrum. The effect of interaction screening on the direct and exchange electronic couplings is also strong. Both these factors significantly affect the dynamics of electron capture and excitation processes. The interaction screening parameter can, thus, be used as a tool for control of the collision dynamics.

Dynamics ofHe2++H(1s)excitation and electron-capture processes in Debye plasmas

Collision dynamics of the ${\mathrm{He}}^{2+}+\mathrm{H}(1s)$ system imbedded in a Debye plasma is studied by the two-center atomic orbital close-coupling (AOCC) method in the energy range $5--300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$. The atomic orbitals and electron binding energies of atomic states are calculated within Debye-H\"uckel approximation of the screened Coulomb potential and used in AOCC dynamics formalism to calculate the state-selective electron capture and excitation cross sections. The basis contained 174 orbitals centered on the target (all $n\ensuremath{\le}6$ discrete states and 117 quasicontinuum states) and 20 orbitals centered on the projectile (all $n\ensuremath{\le}4$ discrete states). It is demonstrated that the screening of Coulomb interactions in the system progressively reduces the number of available excitation and electron capture channels when the screening parameter increases. The screening of Coulomb interactions introduces changes also in the values of direct and exchange couplings, thus affecting the magnitude and energy behavior of the cross sections. The control of dynamics of collision processes in a Debye plasma by varying the plasma screening of Coulomb interactions in the collision system is discussed.

State-Selective Electron Capture for keV He2+ Ions onHelium Collisions Studied by Recoil Momentum Spectroscopy

State-selective single electron capture cross sections are measured byrecoil ion momentum spectroscopy technique for He2+ on He at30 keV incident energy. The cross sections for capture into ground andexcited states are obtained and compared to classical modelcalculations as well as to the quantum mechanical calculations. Theexperimental results are in good agreement with quantum mechanicalresults.